<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.
</abstract>

In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.

Frames associated with shift invariant spaces on positive half line

Department of Mathematics, Faculty of Science

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Frames associated with shift invariant spaces on positive half line"}

In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in...

Frames associated with shift invariant spaces on positive half line

Publié en ligne: 26 août 2021

Pages: 23 - 44

Reçu: 28 août 2020

DOI: https://doi.org/10.2478/ausm-2021-0002

Mots clés
shift-invariant space, Walsh wavelet frame, Gabor frame, Walsh-Fourier transform

© 2021 Owais Ahmad et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Frames associated with shift invariant spaces on positive half line

Publié en ligne: 26 août 2021

Pages: 23 - 44

Reçu: 28 août 2020

DOI: https://doi.org/10.2478/ausm-2021-0002

Mots clésshift-invariant space, Walsh wavelet frame, Gabor frame, Walsh-Fourier transform

© 2021 Owais Ahmad et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
shift-invariant space, Walsh wavelet frame, Gabor frame, Walsh-Fourier transform